Study on BPC Permutation Ability and Fault Tolerant Ability of Hypercube Networks

研究了故障超立方体中的二维可连通子立方体分配问题。研究了n-立方体是否存在2个m维不交的无错子立方体.在实际应用中，较大的m值更有效，因此首先检查m=n-2的情况。通过给出“n-立方中至少存在两个无故障（n-2）-子立方的故障数不超过n-1”的性质，得到了“n-立方中至少存在两个无故障（n-i-2）-子立方的故障数不超过2^i（n-i+1）-2”的性质.其次，研究了两个子立方体之间不相交路径的个数。这个数字表示这些子立方体之间的通信永远不会被切断的最大故障数。然后，讨论了当两个无故障子立方体存在时，这两个无故障子立方体之间的通信是否总是可用的。本文给出了一种解决方案，即建立一个系统，使得在（m+1）-子立方体中执行的正则超立方体算法，即使在（m +1）-子立方体发生故障的情况下，仍能由两个无故障的、不相交的、可通信的m-子立方体执行，而不发生任何退化。

Dimensional communicable 2 subcubes allocation problems in faulty hypercubes are studied in this research. An n-cube is investigated on whether the faulty n-cube possesses 2 m-dimensional disjoint fault-free subcubes or not. Larger values of m is more efficient in practical uses, so the case of m=n-2 is first examined. By giving a property of "the number of faults on an n-cube in which there always exist at least two fault-free (n-2) -subcubes is not over n-1", we obtained a property of "The number of faults located on an n-cube in which there always exist at least two fault-free (n-i-2) -subcubes is not over 2^i (n-i+1) -2". Next, the number of disjoint paths between the two subcubes is investigated. This number suggests the maximum number of faults by which the communication between these subcubes is never cut off. Then, whether the communication between two fault-free subcubes is always available or not when these two fault-free subcubes exist was discussed. This discussion gives a solution to establish a system where a regular hypercube alogrithm executing in an (m+1) -subcube still be executed by two fault-free disjoint communicable m-subcubes without any degradation even if the (m+1) -subcube becomes faulty.